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arXiv · 2010.10277

Compact embedding theorems and a Lions' type Lemma for fractional Orlicz-Sobolev spaces

Edcarlos D. Silva·Marcos L. M. Carvalho·José Carlos de Albuquerque·Sabri Bahrouni
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Abstract

In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the weight is unbounded. We also obtain a version of Lions' "vanishing" Lemma for fractional Orlicz-Sobolev spaces, by introducing new techniques to overcome the lack of a suitable interpolation law. Finally, as a product of the abstract results, we use a minimization method over the Nehari manifold to prove the existence of ground state solutions for a class of nonlinear Schrödinger equations, taking into account unbounded or bounded potentials.

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Edcarlos D. Silva, Marcos L. M. Carvalho, José Carlos de Albuquerque, Sabri Bahrouni. 2020-10-20. Compact embedding theorems and a Lions' type Lemma for fractional Orlicz-Sobolev spaces. https://arxiv.org/abs/2010.10277

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